Solution of a nonlinear singular integral equation with quadratic nonlinearity - Gun’ko, O. V. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
Using methods of the theory of boundary-value problems for analytic functions, we prove a theorem on the existence of solutions of the equation u^2 ( t ) + ( 1π _ - ∞ ^∞ u( τ ) τ - t dτ )^2 = A^2 ( t ) and determine the general form of a solution by using zeros of an entire function A^2 (z) of exponential type.